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Math Help - Partial Fraction Equation

  1. #1
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    Partial Fraction Equation

    if f(x) = x-3/(x+4)(x^2-2), express f(x) in partial fraction

    x-3/(x+4)(x^2-2) = A/(x+4) + (Bx+C)/(x^2-2)

    x-3 = A(x^2-2) + (Bx + C)(x+4)

    if x = -4
    -4-3 = A((-4)^2-2) + (B(-4) + C)(-4 + 4)
    -7 = 14A, A=-1/2

    if x=0,
    0-3 = A(-2) + (B(0) + C)(4)
    -3 = -2A + 4C
    -3 = -2(-1/2) + 4C
    -3 +1 = 4C
    C= -1/2

    if x=2
    2-3 = A(2) + (B(2) + C)(6)
    -1 = (-1/2)(2) + 12B + 6(-1/2)
    -1 = -1 +12B -3
    -1+4 = 12B
    B = 1/3

    therefore, x-3/(x+4)(x^2-2) = -1/2(x+4) + ((1/4)(x) + (-1/2))/(x^2-2)

    = -1/2(x+4) + (x-2)/4(x^2-2)

    This is the final answer i get, but some how in the text book the answer given is

    = -1/2(x+4) + (x-2)/2(x^2-2)

    Do you mind to let me know is my did wrongly or the answer provided is wrong.

    thank you.
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  2. #2
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